# Advanced Math Help with Any Problems!

Messiah Sutton 2022-11-09

## The velocity distribution for laminar flow between parallel plates is given by:$\frac{u}{{u}_{max}}=1-{\left(\frac{2y}{h}\right)}^{2}$where h is the distance separating the plates and the origin is placed midway between the plates. Consider a flow of water at ${15}^{\circ }C$ , with ${u}_{max}=0.30\frac{m}{sec}$ and . Calculate the shear stress on the upper plate and give its direction.

Jared Lowe 2022-11-05

## How to arrive at this integral?However, I am not sure how to arrive at this:$\begin{array}{rl}\phantom{=}& {\int }_{0}^{1}{x}^{n+2}\left(1-x{\right)}^{n}\phantom{\rule{thinmathspace}{0ex}}dx+2{\int }_{0}^{1}{x}^{n+1}\left(1-x{\right)}^{n+1}\phantom{\rule{thinmathspace}{0ex}}dx+{\int }_{0}^{1}{x}^{n}\left(1-x{\right)}^{n+2}\phantom{\rule{thinmathspace}{0ex}}dx\\ =& 2I\left(n+1\right)+2{\int }_{0}^{1}{x}^{n+2}\left(1-x{\right)}^{n}\phantom{\rule{thinmathspace}{0ex}}dx\end{array}$and why the highlighted part is equal to each other? What type of integral is that?

MMDCCC50m 2022-11-05

## Find a recursion formula for combinatorial problemLet ${C}_{n}$ be the number of sequences with a length of n, which their elements belong to {0,1,2}, and they don't contain the following sequences: 11,21. Find a recursion formula with starting conditions for ${C}_{n}$.

Noe Cowan 2022-11-02

## What is the most general distribution for which $E\left[1/x\right]=1/E\left[x\right]$?What is the most general distribution for which the expected value of the multiplicative inverse equals the multiplicative inverse of the expected value?Motivation: I'm into modelling dynamics on graphs and I found a problem which is easily solvable in cases where the degree distribution of the vertices is a distribution where $E\left[1/k\right]=1/E\left[k\right]$. (${k}_{i}$ is the degree of the ith vertex) From this solution I may gain an insight into how to unify multiple models.So particularly I'm looking for a distribution which consists of non-negative, finite integers. But I'm also interested in continuous solutions. Distributions where $E\left[1/{k}^{n}\right]=1/E\left[{k}^{n}\right]$ may also help unifying the models.What I do know so far, that ${k}_{i}=1$ is a particular solution. In the continuous case every function where $f\left(x\right)=f\left(1/x\right)$ and $E\left[x\right]=1$ is a solution. I know what momentum generating functions are and they seem like a good direction to try in, but I failed so far.What is the most general form of this distribution? Does it have a name? It sounds like something trivial, like a "famous" distribution, but I can't find it.

Joglxym 2022-11-02

## Let $f:A\to B$ and $g:C\to D$. DefineProve that $f×g$ is a function from $A×C$ to $B×D$.My proof (so far):Let $\left(a,c\right)\in A×C$, then $a\in A$ and $c\in C$.Let $\left(b,d\right)\in B×D$, $b\in B$ and $d\in D$.If $p\in A×C$ then $p=\left(a,c\right)$.Define $\left(f×g\right)\left(p\right)$ as $\left(f×g\right)\left(p\right)=\left(f×g\right)\left(a,c\right)=\left(f\left(a\right),g\left(c\right)\right)=\left(b,d\right)$, however $b\in B$ and $d\in D$ and $\left(b,d\right)\in B×D$.This shows $f×g$ is a function from $A×C$ to $B×D$ as $\left(f×g\right):A×C\to B×D$ then $\left(a,b\right)\to \left(f\left(a\right),g\left(c\right)\right)$.I know that it is not well written out, but I was wondering if my thought process so far made sense or if I accidentally missed something. Additionally, I am unsure of what the next step may be. As a sidenote, I am worried that this does not work for the given definition of $f×g$.

Upper Level MathOpen question
pancho ono2022-10-29
Upper Level MathOpen question
Benu Sharma2022-10-28

## In August 2013, E*TRADE Financial was offering only 0.05% interest on its online checking accounts, with interest reinvested monthly. Find the associated exponential model for the value of a \$5000 deposit after "t" years. Assuming that this rate of return continued for 7 years, how much would a deposit of \$5000 in August 2013 be worth in August 2020? (Answer to the nearest \$1. )

Maribel Vang 2022-10-28

## Extracting even / odd part of summation trickGiven a function f(x), we know its even part is given as $\frac{f\left(x\right)+f\left(-x\right)}{2}$ and its odd part is given by $\frac{f\left(x\right)-f\left(-x\right)}{2}$.Consider a discrete sequence given by ${a}_{j}$ for $j\ge 1$, then the sum of the terms in the sequence till n terms is given as$S=\sum _{j}^{n}{a}_{j}$Suppose I wanted to get the sum of the even terms in the above expression; then${S}_{odd}=\sum _{j}^{n}\frac{{a}_{-j}+{a}_{j}}{2}$and, for odd,${S}_{odd}=\sum _{j}^{n}\frac{{a}_{j}-{a}_{-j}}{2}$But wait, our sequence was defined for $j\ge 1$. Well, here's the thing: ${a}_{j}$ is some function of j, extending the domain to negative integers and evaluating the function gives the right answer... but I can't understand why the continuous function trick extended to here.Examples:Sum of first n numbers given as $\frac{n\left(n+1\right)}{2}$, sum of first n odds will be given as: $\frac{n\left(n+1\right)}{2}-\frac{n\left(1-n\right)}{2}$My attempt at finding an exact connection: To the discrete sequence $\frac{n\left(n+1\right)}{2}$, we can associate a function $f\left(x\right)=\frac{x\left(x+1\right)}{2}$ and we can think of the summation as summing this function at several different input points i.e:$S=\sum _{j}^{n}{a}_{j}\to \sum _{k}^{n}f\left(x+k\right)$Then we apply the even odd decomposition and return back to the sequence world.My question: Does there exist an association for every sequence with a function? If not, what is the criterion for an association to exist?

Upper Level MathOpen question
pancho ono2022-10-26
Upper Level MathOpen question
pancho ono2022-10-26
Upper Level MathOpen question
pancho ono2022-10-26
Upper Level MathOpen question
pancho ono2022-10-25
Discrete mathOpen question
pancho ono2022-10-25
Discrete mathOpen question
Ryan Banks2022-10-17

## what is 45 as a fraction

Upper Level MathOpen question
Anyangwa Emmanuel Atekwana2022-10-16

## Write an equivalent first-order differential equation and initial condition for yy=−1+∫x1(t−y(t))dt

Upper Level MathOpen question
Lindy Mandawe2022-10-15

## Is {8} ∈ {{8}, {8}}?

Upper Level MathOpen question
JUNSANG YOON2022-10-07